@inproceedings{c0541515dcd24605bded28b350114b87,

title = "The Parametrized Complexity of the Segment Number",

abstract = "Given a straight-line drawing of a graph, a segment is a maximal set of edges that form a line segment. Given a planar graph G, the segment number of G is the minimum number of segments that can be achieved by any planar straight-line drawing of G. The line cover number of G is the minimum number of lines that support all the edges of a planar straight-line drawing of G. Computing the segment number or the line cover number of a planar graph is ∃ R -complete and, thus, NP-hard. We study the problem of computing the segment number from the perspective of parameterized complexity. We show that this problem is fixed-parameter tractable with respect to each of the following parameters: the vertex cover number, the segment number, and the line cover number. We also consider colored versions of the segment and the line cover number.",

keywords = "Line cover number, Parameterized complexity, Segment number, Vertex cover number, Visual complexity",

author = "Sabine Cornelsen and {Da Lozzo}, Giordano and Luca Grilli and Siddharth Gupta and Jan Kratochv{\'i}l and Alexander Wolff",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 31st International Symposium on Graph Drawing and Network Visualization, GD 2023 ; Conference date: 20-09-2023 Through 22-09-2023",

year = "2023",

month = jan,

day = "1",

doi = "10.1007/978-3-031-49275-4_7",

language = "English",

isbn = "9783031492747",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Science and Business Media Deutschland GmbH",

pages = "97--113",

editor = "Bekos, {Michael A.} and Markus Chimani",

booktitle = "Graph Drawing and Network Visualization - 31st International Symposium, GD 2023, Revised Selected Papers",

address = "Germany",

}